The Physics of Forward Time travel
Do you know that you are time traveling right now? The act of time traveling merely involves movement through time. We pay little attention to this concept in our everyday lives because it appears that everyone is moving though time at the same rate. This page will address this misconception and demonstrate how traveling through time at different rates can and does occur.
The physics of forward time travel and backward time travel are different. This page will focus on the physics of forward time travel, which is considerably less complex. To begin our journey, we will first need some background on Einstein’s Special Theory of Relativity.
Frames of Reference
Einstein’s theory relies on frames of reference. If you are sitting and reading this, your frame of reference is from the chair you are in. If you were to get up and walk to your door, your frame of reference would move with you. Frames of reference are used to evaluate the motion of objects. Motion in the universe is relative to frames of reference. The following example demonstrates this concept.
Bob is standing on the subway platform. John is on the subway that is approaching the platform. From Bob’s frame of reference, Bob is stationary because he is standing in one location on the platform. From John’s frame of reference, John is stationary because he is standing in one location on the subway.
As the subway travels past Bob’s platform, John and Bob see each other. From Bob’s frame of reference, John is moving forward. From John’s frame of reference, Bob is moving backwards.
The Speed of Light
A fundamental postulate of Einstein’s Special Theory of Relativity is that the laws of physics hold true for all inertial frames of references. Light is electromagnetic radiation which is governed by the laws of electrodynamics. Since the laws of electrodynamics hold true for all inertial frames of references, then the speed of light is going to be constant. The speed of light is generally denoted by a c which is equal to 299,792,458 meters per second. (This is usually rounded to 3 x 108 meters per second.) So no matter if you are standing still or on a spaceship flying at a constant velocity close to the speed of light, you will see light moving at this speed.
Assume the subway was moving at 100 meters per second. Right before the subway passes by Bob, John rolls a ball to the front of the subway at a speed of 50 meters per second.
Question 1: How fast does John see the ball traveling? answer
Question 2: How fast does Bob see the ball traveling? answer
Now instead of rolling a ball, John turns on a flashlight right before the subway passes by Bob. Remember our discussion of the speed of light before answering the next two questions.
Question 3: How fast does John see the light traveling out of the flashlight? answer
Question 4: How fast does Bob see the light traveling out of the flashlight? answer
No matter the frame of reference, the speed of light is constant.
Time Dilation
With this understanding, we can now address how forward time travel is possible. We will use an example to demonstrate the connection.
An observer is standing on the Earth and sees a spaceship fly overhead at 0.8c (about 2.4 x 108 meters per second). On the space ship are an astronaut and a set of two mirrors facing each other. The mirrors are 0.9m apart from each other. It takes 3 nanoseconds for a light beam to cover 0.9m. As the spaceship passes overhead the astronaut flashes a light so that it hits the bottom mirror, reflects off the top mirror, and then back to the bottom mirror. It takes the light 6 nanoseconds to make the roundtrip. This is from the frame of reference of the astronaut.
The observer on earth will see a different situation. Since the mirrors are moving past him near the speed of light, he doesn't see the light moving straight up and down but instead at a diagonal. According to the diagram above, the light now has to travel 1.5m to reach the opposite mirror. Since light has a constant speed and the distance is increasing, then the time it takes the light to make a round trip increases also. This is using the equation v = d/t. To the observer, the roundtrip of the light beam between the two mirrors takes 10 nanoseconds. This creates a ratio of 10 to 6 for the time it takes the light beam to make a round trip between the two mirrors from the frame of reference of the observer on the earth and the frame of reference of the astronaut on the spaceship.
You are now probably wondering how this connects with time travel. It does so through the phenomenon of time dilation. First, assume that to the astronaut, his heart beats every second. Using 6 nanoseconds per roundtrip, the astronaut’s heart will beat every 1.66 x 108 round trips. No matter the frame of reference, his heart will beat every 1.66 x 108 round trips.
To the observer on earth, the astronaut’s heart beats every 1.66 x 108 round trips. Using 10 nanoseconds per round trip, he will observe the astronaut’s heart beat every 1.66 seconds. If we associate the rate of the heart beat with the rest of their bodily functions, we can say that the rate of the heart beat is directly proportional to the rate of aging of that individual.
Now let’s assume that to the observer is initially the same age as the astronaut and his heart beats once every second relative to his own frame of reference. When he looks at the astronaut, he sees the astronaut aging at the rate of one heart beat per 1.66 seconds. For every 10 heart beats of the observer, he will observe that the astronaut’s heart beats only 6 times. So when the observer has aged one year, he will have seen the astronaut age only 0.6 years.
Forward Time Travel and the Twin Paradox
This doesn't yet quite amount to time travel. From the observer's frame of reference the astronaut is aging more slowly. But, from the astronaut's frame of reference, the observer is aging more slowly. It would be a stretch of our ordinary understanding of time travel to count this as a case of time travel.
To have described a more or less clear case of time travel, we need just one more complication. Suppose that the astronaut travels past the Earth and, just as he does, he and the observer are exactly the same age, maybe having even experienced the exact same number of heartbeats. Let's assume that the astronaut travels at 80% of the speed of light to a location 4 light years away. As the observer sees it, the trip takes 5 years. Due to the effects of time dilation, relative to the observer's frame of reference, the astronaut will age 3 years. The return trip will be basically the same story. Now, the astronaut is traveling in a different direction, but, for the observer, the astronaut is moving and so continues to experience the effects of time dilation. Only three more years pass for the astronaut, while 5 more pass for the observer. Now it seems pretty clear that the astronaut has time traveled to the future. He is like the astronauts in the Planet of the Apes, who unbeknownst to them make a round trip to Earth of the distant future.
The famous twin paradox arises because it can seem that parallel calculations should apply to the Earth-bound observer from the astronaut's frame of reference, absurdly resulting in the conclusion that the astronaut and the observer each end up younger than the other. That, however, is not the case. It is only a minor idealization to think of the observer as in an inertial frame of reference. (That only involves ignoring the effects of gravity and the motion of Earth.) But the astronaut has to be considered as occupying two different inertial frames, because of his change of direction. We won't go into the details, but it turns out that, for the second leg of the trip, from this second frame of reference, the astronaut's departure will be simultaneous with 8.2 years having passed for the observer on Earth and so 10 years will have passed for the observer when the astronaut arrives on Earth (Gott 2001, 66-69). Both the astronaut and the observer will judge ten years to have passed for the observer.
This is not just so much theorizing. The effects of time dilation have been empirically tested many different ways. In one famous and simple experiment, performed in 1971, scientists Joe Hafele and Richard Keating put four atomic clocks on an east-bound flight around the world and then compared them to reference clocks left at their point of departure. Upon completing the trip, the clocks from the flight were 59 nanoseconds behind the reference clocks, as theory predicts.
Resources
Bonsor, Kevin. "How Time Travel Will Work" HowStuffWorks (October 2000).
Davies, Paul. How to Build a Time Machine. New York: Penguin Books, 2001.
Gott, J. Richard. Time Travel in Einstein's Universe. Boston: Houghton-Mifflin, 2001.
Groleau, Rick. "Think Like Einstein" Nova Online | Time Travel (October 1999).